Calculus Examples Differential Equations

Find the Values of k that Satisfy the Differential Equation

$5 x^{2} y' - 2 y + 4 = 0$ , $y = k$

Step 1

Find $y'$ .

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Step 1.1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (k)$

Step 1.2

The derivative of $y$ with respect to $x$ is $y'$ .

$y'$

Step 1.3

Since $k$ is constant with respect to $x$ , the derivative of $k$ with respect to $x$ is $0$ .

$0$

Step 1.4

Reform the equation by setting the left side equal to the right side.

$y' = 0$

Step 2

Substitute into the given differential equation.

$5 x^{2} \cdot 0 - 2 k + 4 = 0$

Step 3

Solve for $k$ .

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Step 3.1

Simplify $5 x^{2} \cdot 0 - 2 k + 4$ .

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Step 3.1.1

Multiply $5 x^{2} \cdot 0$ .

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Step 3.1.1.1

Multiply $0$ by $5$ .

$0 x^{2} - 2 k + 4 = 0$

Step 3.1.1.2

Multiply $0$ by $x^{2}$ .

$0 - 2 k + 4 = 0$

Step 3.1.2

Subtract $2 k$ from $0$ .

$- 2 k + 4 = 0$

Step 3.2

Subtract $4$ from both sides of the equation.

$- 2 k = - 4$

Step 3.3

Divide each term in $- 2 k = - 4$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 k = - 4$ by $- 2$ .

$\frac{- 2 k}{- 2} = \frac{- 4}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 k}{- 2} = \frac{- 4}{- 2}$

Step 3.3.2.1.2

Divide $k$ by $1$ .

$k = \frac{- 4}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 4$ by $- 2$ .

$k = 2$

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Find the Values of k that Satisfy the Differential Equation

Differential Equations

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