38.2.45 problem 45

Internal problem ID [6474]
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
Date solved : Monday, January 27, 2025 at 02:07:09 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.179 (sec). Leaf size: 23

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

\[ y = \frac {x^{3}+3 c_1 +3 x}{3 \sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 29

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

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