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 : Sunday, March 30, 2025 at 11:01:16 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 18

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

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

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

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

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

✓ Sympy. Time used: 0.335 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*y(x) - 5*x + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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