32.2.44 problem 45

Internal problem ID [7761]
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 : Tuesday, September 30, 2025 at 05:05:01 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 29

ode=(1+x^2)*D[y[x],x]+x*y[x]==(1+x^2)^(3/2); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.284 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) - (x**2 + 1)**(3/2) + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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