Internal problem ID [4550]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order.
page 315
Problem number: 10.3.5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2 y x -\sinh \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 16
dsolve([x^2*diff(y(x),x)+2*x*y(x)=sinh(x),y(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\cosh \relax (x )+2-\cosh \relax (1)}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 17
DSolve[{x^2*y'[x]+2*x*y[x]==Sinh[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\cosh (x)+2-\cosh (1)}{x^2} \\ \end{align*}