37.2.4 problem 10.3.5

Internal problem ID [6401]
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
Date solved : Monday, January 27, 2025 at 02:00:35 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

dsolve([x^2*diff(y(x),x)+2*x*y(x)=sinh(x),y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {\cosh \left (x \right )+2-\cosh \left (1\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 17

DSolve[{x^2*D[y[x],x]+2*x*y[x]==Sinh[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\cosh (x)+2-\cosh (1)}{x^2} \]