67.2.30 problem Problem 5(d)

Internal problem ID [13987]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 5(d)
Date solved : Tuesday, January 28, 2025 at 06:11:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✗ Solution by Maple

dsolve([x*diff(y(x),x$2)+2*x^2*diff(y(x),x)+y(x)*sin(x)=sinh(x),y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{x^2*D[y[x],{x,2}]+2*x^2*D[y[x],x]+y[x]*Sin[x]==Sinh[x],{y[0]==1,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved