2.41 problem 41

Internal problem ID [4619]

Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 41.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (-x^{3}+1\right ) y^{\prime }+y x^{2}-x^{2} \left (-x^{3}+1\right )=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve((1-x^3)*diff(y(x),x)+x^2*y(x)=x^2*(1-x^3),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{3}}{2}-\frac {1}{2}+\left (x^{3}-1\right )^{\frac {1}{3}} c_{1} \]

Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 27

DSolve[(1-x^3)*y'[x]+x^2*y[x]==x^2*(1-x^3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (x^3+2 c_1 \sqrt [3]{x^3-1}-1\right ) \\ \end{align*}