38.2.33 problem 33

Internal problem ID [6462]
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 : 33
Date solved : Monday, January 27, 2025 at 02:06:10 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \sqrt {x^{2}+1}\, c_1 -1 \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 24

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

\begin{align*} y(x)\to -1+c_1 \sqrt {x^2+1} \\ y(x)\to -1 \\ \end{align*}