# Solve the following differential equation. {eq}\displaystyle y' = \sin^2 (3 x - 3 y + 1) {/eq}

## Question:

Solve the following differential equation.

{eq}\displaystyle y' = \sin^2 (3 x - 3 y + 1) {/eq}

## Separable Differential Equation:

If we have a first-order and first-degree differential equation defined as {eq}\dfrac{dy}{dx} = f(a_1x + a_2 y + a_3) {/eq} then in order to reduce this differential equation into a separable form we have to substitute {eq}v= a_1x + a_2 y+ a_3\\ \implies a_1 + a_2 f(v) = \dfrac{dv}{dx}\; \text{and the solution is given by }\; \int \dfrac{dv}{a_1 + a_2 f(v) } = \int dx + a_3. {/eq}

## Answer and Explanation: 1

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We are given a differential equation

{eq}\displaystyle y' = \sin^2 (3 x - 3 y + 1) {/eq}

Step 1:

Let {eq}3x-3y+1 = v\\ \text{differentiate with...

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