Internal problem ID [4623]
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: 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+y x -\left (x^{2}+1\right )^{\frac {3}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((1+x^2)*diff(y(x),x)+x*y(x)=(1+x^2)^(3/2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {1}{3} x^{3}+x +c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 29
DSolve[(1+x^2)*y'[x]+x*y[x]==(1+x^2)^(3/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3+3 x+3 c_1}{3 \sqrt {x^2+1}} \\ \end{align*}