38.2.14 problem 14

Internal problem ID [6443]
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 : 14
Date solved : Monday, January 27, 2025 at 02:04:16 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 18

dsolve([(1+x^2)*diff(y(x),x)+3*x*y(x)=5*x,y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {5}{3}+\frac {2 \sqrt {2}}{3 \left (x^{2}+1\right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 27

DSolve[{(1+x^2)*D[y[x],x]+3*x*y[x]==5*x,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 \sqrt {2}}{3 \left (x^2+1\right )^{3/2}}+\frac {5}{3} \]