anonymous one year ago Show that xy^3-xy^3sin(x)= 1 is an implicit solution to the following $dy/dx = ((xcos(x) + \sin(x) - 1)y)/(3(x-xsin(x)))$

• This Question is Open
1. SolomonZelman

$$\large\color{black}{ \displaystyle xy^3-xy^3\sin(x)= 1 }$$ Rearrangement: $$\large\color{black}{ \displaystyle 1/y^3=x-x\sin(x) }$$ Calculating dy/dx: $$\large\color{black}{ \displaystyle y'\times \left(-3/y^2\right)=1-(\sin(x) +x\cos(x))}$$ then rearrange it and solve for y'.