Internal problem ID [4580]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{3}+1\right ) y^{\prime }-y x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 15
dsolve([(1+x^3)*diff(y(x),x)=x^2*y(x),y(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = 2^{\frac {2}{3}} \left (x^{3}+1\right )^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 20
DSolve[{(1+x^3)*y'[x]==x^2*y[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2^{2/3} \sqrt [3]{x^3+1} \\ \end{align*}