38.2.41 problem 41

Internal problem ID [6470]
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
Date solved : Monday, January 27, 2025 at 02:06:59 PM
CAS classification : [_linear]

\begin{align*} \left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (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)
 

\[ y = \frac {x^{3}}{2}-\frac {1}{2}+\left (x^{3}-1\right )^{{1}/{3}} c_1 \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 27

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

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