82.41.3 problem Ex. 4

Internal problem ID [18885]
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 : Monday, March 31, 2025 at 06:18:13 PM
CAS classification : [[_2nd_order, _quadrature]]

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

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

ode:=diff(diff(y(x),x),x) = x^2*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*sin(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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