82.41.3 problem Ex. 4

Internal problem ID [18956]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 96
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:38:21 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)=x^2*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-x^{2}+6\right ) \sin \left (x \right )+c_{1} x -4 x \cos \left (x \right )+c_{2} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 26

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

\[ y(x)\to -\left (x^2-6\right ) \sin (x)-4 x \cos (x)+c_2 x+c_1 \]