What is the solution for (dy)/(dx)=y^2e^xsin(3x),y(0)=1 ?

The solution for (dy)/(dx)=y^2e^xsin(3x),y(0)=1 is y=-(10)/(-3e^xcos(3x)+e^xsin(3x)-7)

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(dy)/(dx)=y^2e^xsin(3x),y(0)=1

\frac{d y}{d x} = y^{2} e^{x} sin (3 x), y (0) = 1

y = - \frac{10}{- 3 e ^{x} cos ( 3 x ) + e ^{x} sin ( 3 x ) - 7}

Solution steps

\frac{d y}{d x} = y^{2} e^{x} sin (3 x)

Solve separable ODE:

y = - \frac{10}{- 3 e ^{x} cos ( 3 x ) + e ^{x} sin ( 3 x ) - 7}

y = - \frac{10}{- 3 e ^{x} cos ( 3 x ) + e ^{x} sin ( 3 x ) - 7}

f (x) = \frac{x ^{2} - 4}{x - 4}

\frac{\partial}{\partial x} (e^{(- x^{2} - y^{2})})

x = 4 t^{2} - 3 t + 11

\frac{d}{d x} (sin^{2} (x) + sin (x))

4 cos (t)

What is the solution for (dy)/(dx)=y^2e^xsin(3x),y(0)=1 ?
The solution for (dy)/(dx)=y^2e^xsin(3x),y(0)=1 is y=-(10)/(-3e^xcos(3x)+e^xsin(3x)-7)