38.2.2 problem 2

Internal problem ID [6431]
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 : 2
Date solved : Monday, January 27, 2025 at 02:02:48 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 20

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

\[ y(x)\to 2^{2/3} \sqrt [3]{x^3+1} \]