2.45 problem 45

Internal problem ID [5131]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.0 (sec). Leaf size: 23

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

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

Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 29

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

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