82.53.3 problem Ex. 3

Internal problem ID [19015]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 118
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:45:41 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(x*diff(y(x),x$2)-diff(y(x),x)+4*x^3*y(x)=x^5,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 27

DSolve[x*D[y[x],{x,2}]-D[y[x],x]+4*x^3*y[x]==x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{4}+c_1 \cos \left (x^2\right )+c_2 \sin \left (x^2\right ) \]