Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70801	Find the Antiderivative	f(x)=6x^5+x^4+2x^2-3	$f (x) = 6 x^{5} + x^{4} + 2 x^{2} - 3$
70802	Integrate Using Trig Substitution	integral of square root of 16-x^2 with respect to x	$\int \sqrt{16 - x^{2}} d x$
70803	Evaluate the Limit	limit as x approaches infinity of (3x)/( square root of x^2+1)	$lim_{x \to \infty} \frac{3 x}{\sqrt{x^{2} + 1}}$
70804	Evaluate the Limit	limit as x approaches 1 of -(x-4)/(x^2-6x+8)	$lim_{x \to 1} - \frac{x - 4}{x^{2} - 6 x + 8}$
70805	Find the Derivative - d/dx	arctan(-x/2)	$\arctan (- \frac{x}{2})$
70806	Evaluate the Integral	integral from 0 to 1/2 of (x^4)/(x-1) with respect to x	$\int_{0}^{\frac{1}{2}} \frac{x^{4}}{x - 1} d x$
70807	Find the Maximum/Minimum Value	f(x)=(x^2)/(x-5)	$f (x) = \frac{x^{2}}{x - 5}$
70808	Find dy/dx	y square root of x+4=xy+8	$y \sqrt{x + 4} = x y + 8$
70809	Find the Center and Radius	3x^2+3y^2-12x+6y+18=0	$3 x^{2} + 3 y^{2} - 12 x + 6 y + 18 = 0$
70810	Evaluate the Integral	integral of (3x^5-x^3+6) with respect to x	$\int (3 x^{5} - x^{3} + 6) d x$
70811	Evaluate the Integral	integral from -3 to 2 of (-3\|x\|) with respect to x	$\int_{- 3}^{2} (- 3 \| x \|) d x$
70812	Find the Center and Radius	(x^2)/9-(y^2)/4=1	$\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
70813	Find the Maximum/Minimum Value	f(x)=3x^5-20x^3	$f (x) = 3 x^{5} - 20 x^{3}$
70814	Find the Domain and Range	f(x)=\|3x\| if -2<=x<0; x^3 if x>=0	$f (x) = {\begin{cases} \| 3 x \| & - 2 \leq x < 0 \\ x^{3} & x \geq 0 \end{cases}$
70815	Find dy/dx	4 square root of y=x-y	$4 \sqrt{y} = x - y$
70816	Evaluate the Integral	integral of (-20x^3-6x^-3) with respect to x	$\int (- 20 x^{3} - 6 x^{- 3}) d x$
70817	Evaluate the Integral	integral of (2+ square root of x+x)/x with respect to x	$\int \frac{2 + \sqrt{x} + x}{x} d x$
70818	Verify the Existence and Uniqueness of Solutions for the Differential Equation	(dy)/(dx) = square root of x-y , (1,1)	$\frac{d y}{d x} = \sqrt{x - y}$ , $(1, 1)$
70819	Solve the Differential Equation	(dy)/(dx)-y=e^xy^2	$\frac{d y}{d x} - y = e^{x} y^{2}$
70820	Solve the Differential Equation	(dy)/(dx)+1/xy=x^4y^2	$\frac{d y}{d x} + \frac{1}{x} y = x^{4} y^{2}$
70821	Verify the Existence and Uniqueness of Solutions for the Differential Equation	(dy)/(dx)=2x^2y^2 , (1,1)	$\frac{d y}{d x} = 2 x^{2} y^{2}$ , $(1, 1)$
70822	Solve the Differential Equation	(dy)/(dx)+2xy=x^2y^2	$\frac{d y}{d x} + 2 x y = x^{2} y^{2}$
70823	Solve the Differential Equation	(dy)/(dx)=y/x-(y/x)^2	$\frac{d y}{d x} = \frac{y}{x} - {(\frac{y}{x})}^{2}$
70824	Solve the Differential Equation	(dy)/(dx)=x+y	$\frac{d y}{d x} = x + y$
70825	Verify the Existence and Uniqueness of Solutions for the Differential Equation	(dy)/(dx)=2x^3y , y(1)=1	$\frac{d y}{d x} = 2 x^{3} y$ , $y (1) = 1$
70826	Solve the Differential Equation	(dy)/(dx)=y/x+y/( square root of xy)	$\frac{d y}{d x} = \frac{y}{x} + \frac{y}{\sqrt{x y}}$
70827	Solve the Differential Equation	x*(dy)/(dx)=y+ square root of xy	$x \cdot \frac{d y}{d x} = y + \sqrt{x y}$
70828	Solve the Differential Equation	(dy)/(dx)=2x square root of y-1	$\frac{d y}{d x} = 2 x \sqrt{y - 1}$
70829	Solve the Differential Equation	(dy)/(dx)=4xe^(-y)	$\frac{d y}{d x} = 4 x e^{- y}$
70830	Approximate Using Euler's Method	(dy)/(dt)=sin(t) , y(0)=1 , t=0.5 , h=0.05	$\frac{d y}{d t} = \sin (t)$ , $y (0) = 1$ , $t = 0.5$ , $h = 0.05$
70831	Solve the Differential Equation	(x+y)dx+(x-y)dy=0	$(x + y) d x + (x - y) d y = 0$
70832	Solve the Differential Equation	(3x^2y+y^2)dx+(x^3+2xy+3)dy=0	$(3 x^{2} y + y^{2}) d x + (x^{3} + 2 x y + 3) d y = 0$
70833	Solve the Differential Equation	(dy)/(dx)+y/x=1	$\frac{d y}{d x} + \frac{y}{x} = 1$
70834	Solve the Differential Equation	(dy)/(dx)=2x^-3	$\frac{d y}{d x} = 2 x^{- 3}$
70835	Solve the Differential Equation	(2x+y)dx+(x+1)dy=0	$(2 x + y) d x + (x + 1) d y = 0$
70836	Approximate Using Euler's Method	(dy)/(dt)=e^t , y(0)=0 , t=1 , h=0.1	$\frac{d y}{d t} = e^{t}$ , $y (0) = 0$ , $t = 1$ , $h = 0.1$
70837	Solve the Differential Equation	y''''''''+y=0	$y'''' + y = 0$
70838	Solve the Differential Equation	(dy)/(dx)+y=sin(x)	$\frac{d y}{d x} + y = \sin (x)$
70839	Solve the Differential Equation	xy^2y''''=x+1	$x y^{2} y'' = x + 1$
70840	Solve the Differential Equation	(sin(y)+x)dx+(xcos(y))dy=0	$(\sin (y) + x) d x + (x \cos (y)) d y = 0$
70841	Solve the Differential Equation	(dy)/(dx)=4x^3y	$\frac{d y}{d x} = 4 x^{3} y$
70842	Solve the Differential Equation	(dy)/(dx)-1/xy=2x	$\frac{d y}{d x} - \frac{1}{x} y = 2 x$
70843	Solve the Differential Equation	(dy)/(dx)=2x-3	$\frac{d y}{d x} = 2 x - 3$
70844	Solve the Differential Equation	(dy)/(dx)+y=e^x	$\frac{d y}{d x} + y = e^{x}$
70845	Solve the Differential Equation	(dy)/(dx)+tan(x)y=1	$\frac{d y}{d x} + \tan (x) y = 1$
70846	Solve the Differential Equation	(dy)/(dx)=y^2	$\frac{d y}{d x} = y^{2}$
70847	Solve the Differential Equation	(dy)/(dx)=9x^2y^2	$\frac{d y}{d x} = 9 x^{2} y^{2}$
70848	Solve the Differential Equation	(dx)/(dt)=x/2 if x(0)=1	$\frac{d x}{d t} = \frac{x}{2}$ if $x (0) = 1$
70849	Solve the Differential Equation	(dy)/(dx)=(x^2)/y	$\frac{d y}{d x} = \frac{x^{2}}{y}$
70850	Solve the Differential Equation	(x^2+y^2)dx+(x^2-xy)dy=0	$(x^{2} + y^{2}) d x + (x^{2} - x y) d y = 0$
70851	Solve the Differential Equation	(dy)/(dx)=3x square root of y	$\frac{d y}{d x} = 3 x \sqrt{y}$
70852	Approximate Using Euler's Method	(dy)/(dt)=e^t , y(0)=1 , t=5 , h=0.5	$\frac{d y}{d t} = e^{t}$ , $y (0) = 1$ , $t = 5$ , $h = 0.5$
70853	Solve the Differential Equation	(dy)/(dx)=2y	$\frac{d y}{d x} = 2 y$
70854	Solve the Differential Equation	x(yd)x-(x+2)dy=0	$x yd x - (x + 2) d y = 0$
70855	Solve the Differential Equation	(dy)/(dt)=9t^2	$\frac{d y}{d t} = 9 t^{2}$
70856	Solve the Differential Equation	(dy)/(dt)=ky	$\frac{d y}{d t} = k y$
70857	Solve the Differential Equation	(dy)/(dx)=3y	$\frac{d y}{d x} = 3 y$
70858	Solve the Differential Equation	(y^2+yx)dx-x^2dy=0	$(y^{2} + y x) d x - x^{2} d y = 0$
70859	Solve the Differential Equation	(dQ)/(ds)=9/7s^(2/7)	$\frac{d Q}{d s} = \frac{9}{7} s^{\frac{2}{7}}$
70860	Solve the Differential Equation	(dy)/(dx)-2y=y^2 , y(0)=3	$\frac{d y}{d x} - 2 y = y^{2}$ , $y (0) = 3$
70861	Solve the Differential Equation	(dy)/(dx)=e^(x+y)	$\frac{d y}{d x} = e^{x + y}$
70862	Solve the Differential Equation	(x+y)dx+xdy=0	$(x + y) d x + x d y = 0$
70863	Solve the Differential Equation	2(yd)x=3xdy	$2 yd x = 3 x d y$
70864	Solve the Differential Equation	y(dy)/(dx)=2/(3x^2)	$y \frac{d y}{d x} = \frac{2}{3 x^{2}}$
70865	Solve the Differential Equation	y''''=x-2xy	$y'' = x - 2 x y$
70866	Solve the Differential Equation	(dy)/(dx)=6x^-7	$\frac{d y}{d x} = 6 x^{- 7}$
70867	Solve the Differential Equation	(dy)/(dx) = square root of xy	$\frac{d y}{d x} = \sqrt{x y}$
70868	Solve the Differential Equation	(dy)/(dx)=(2x)/y	$\frac{d y}{d x} = \frac{2 x}{y}$
70869	Solve the Differential Equation	(x^2+y^2)dx+x(yd)y=0	$(x^{2} + y^{2}) d x + x yd y = 0$
70870	Solve the Differential Equation	(x-y)dx+xdy=0	$(x - y) d x + x d y = 0$
70871	Solve the Differential Equation	(dy)/(dx)=5x square root of y	$\frac{d y}{d x} = 5 x \sqrt{y}$
70872	Solve the Differential Equation	3(3x^2+y^2)dx-2x(yd)y=0	$3 (3 x^{2} + y^{2}) d x - 2 x yd y = 0$
70873	Solve the Differential Equation	(dy)/(dx)=x-5	$\frac{d y}{d x} = x - 5$
70874	Solve the Differential Equation	(dz)/(dt)+e^(t+z)=0	$\frac{d z}{d t} + e^{t + z} = 0$
70875	Solve the Differential Equation	(dy)/(dx)=8x^-9	$\frac{d y}{d x} = 8 x^{- 9}$
70876	Solve the Differential Equation	xy^3dx+e^(x^2)dy=0	$x y^{3} d x + e^{x^{2}} d y = 0$
70877	Solve the Differential Equation	(dy)/(dx)=(4x-1)/(3y+2)	$\frac{d y}{d x} = \frac{4 x - 1}{3 y + 2}$
70878	Solve the Differential Equation	(5x+4y)dx+(4x-8y^3)dy=0	$(5 x + 4 y) d x + (4 x - 8 y^{3}) d y = 0$
70879	Solve the Differential Equation	(dy)/(dx)=9x square root of y	$\frac{d y}{d x} = 9 x \sqrt{y}$
70880	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y^2)	$\frac{d y}{d x} = \frac{x^{2}}{y^{2}}$
70881	Solve the Differential Equation	(dy)/(dx)=4y	$\frac{d y}{d x} = 4 y$
70882	Solve the Differential Equation	y''''''''-y=0	$y'''' - y = 0$
70883	Solve the Differential Equation	(dy)/(dx)=(x-5)	$\frac{d y}{d x} = (x - 5)$
70884	Solve the Differential Equation	(dy)/(dx)=4x^-5	$\frac{d y}{d x} = 4 x^{- 5}$
70885	Solve the Differential Equation	(dy)/(dx)-(3y)/x=x^3	$\frac{d y}{d x} - \frac{3 y}{x} = x^{3}$
70886	Solve the Differential Equation	3y-x(dy)/(dx)=6	$3 y - x \frac{d y}{d x} = 6$
70887	Solve the Differential Equation	(dy)/(dx)=x^2	$\frac{d y}{d x} = x^{2}$
70888	Solve the Differential Equation	x(dy)/(dx)+y=1/(y^2)	$x \frac{d y}{d x} + y = \frac{1}{y^{2}}$
70889	Solve the Differential Equation	(1+x)dy-(yd)x=0	$(1 + x) d y - yd x = 0$
70890	Solve the Differential Equation	y''''+y=0	$y'' + y = 0$
70891	Solve the Differential Equation	(x^5+3y)dx-xdy=0	$(x^{5} + 3 y) d x - x d y = 0$
70892	Solve the Differential Equation	(dy)/(dx)=(6x^2)/(2y+cos(y))	$\frac{d y}{d x} = \frac{6 x^{2}}{2 y + \cos (y)}$
70893	Solve the Differential Equation	(dy)/(dx)=x-y	$\frac{d y}{d x} = x - y$
70894	Solve the Differential Equation	e^xy(dy)/(dx)=e^(-y)+e^(-2x-y)	$e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}$
70895	Solve the Differential Equation	2y(dy)/(dx)=(cos(x))/(1+sin(x))	$2 y \frac{d y}{d x} = \frac{\cos (x)}{1 + \sin (x)}$
70896	Solve the Differential Equation	(dy)/(dx)=x	$\frac{d y}{d x} = x$
70897	Solve the Differential Equation	x(yd)x+(x^2+y^2)dy=0	$x yd x + (x^{2} + y^{2}) d y = 0$
70898	Solve the Differential Equation	x^2dx+y(x-1)dy=0	$x^{2} d x + y (x - 1) d y = 0$
70899	Solve the Differential Equation	(x-2y)dx+2(y-x)dy=0	$(x - 2 y) d x + 2 (y - x) d y = 0$
70900	Solve the Differential Equation	e^y(dy)/(dx)=(2 natural log of x)/x	$e^{y} \frac{d y}{d x} = \frac{2 \ln (x)}{x}$