Solve (y^{2}e^{xy^{2}}+4y^3)dx+(2xye^xy^2-3y^2)dy=

$$( y ^ { 2 } e ^ { x y ^ { 2 } } + 4 y ^ { 3 } ) d x + ( 2 x y e ^ { x y ^ { 2 } } - 3 y ^ { 2 } ) d y =$$

Factor

$$dy^{2}\left(x\left(4y+3e^{xy^{2}}\right)-3y\right)$$

Solution Steps

Factor out d.

$$d\left(\left(y^{2}e^{xy^{2}}+4y^{3}\right)x+\left(2xye^{xy^{2}}-3y^{2}\right)y\right)$$

Evaluate

$$dy^{2}\left(x\left(4y+3e^{xy^{2}}\right)-3y\right)$$