2.14 problem 14

Internal problem ID [4592]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+3 x y-5 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}

Solution by Maple

Time used: 0.019 (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)
 

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

Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 27

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

\begin{align*} y(x)\to \frac {2 \sqrt {2}}{3 \left (x^2+1\right )^{3/2}}+\frac {5}{3} \\ \end{align*}