What is the solution for yy^'=x^2e^{2x+2y}sin(3x) ?

The solution for yy^'=x^2e^{2x+2y}sin(3x) is y=-(\W((integral of e^{2x}x^2sin(3x)*4)/e))/(2)-1/2

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yy^'=x^2e^{2x+2y}sin(3x)

y y^{^{'}} = x^{2} e^{2 x + 2 y} sin (3 x)

y = - \frac{W ( \frac{\int e ^{2 x} x ^{2} s i n ( 3 x ) d x \cdot 4}{e} )}{2} - \frac{1}{2}

Solution steps

y y^{'} (x) = x^{2} e^{2 x + 2 y} sin (3 x)

Solve separable ODE:

y = - \frac{W ( \frac{\int e ^{2 x} x ^{2} s i n ( 3 x ) d x \cdot 4}{e} )}{2} - \frac{1}{2}

y = - \frac{W ( \frac{\int e ^{2 x} x ^{2} s i n ( 3 x ) d x \cdot 4}{e} )}{2} - \frac{1}{2}

x \cdot \frac{d y}{d x} = 2 + 3 y

\frac{d x}{d t} + \frac{1}{50} x = 4

5 y d x = 3 x d y

\frac{d x}{d k} + a x (k) = b

y^{^{'}} - \frac{cos ( x )}{e ^{y}} = 0

What is the solution for yy^'=x^2e^{2x+2y}sin(3x) ?
The solution for yy^'=x^2e^{2x+2y}sin(3x) is y=-(\W((integral of e^{2x}x^2sin(3x)*4)/e))/(2)-1/2