58.2.24 problem 25

Internal problem ID [9147]
Book : Second order enumerated odes
Section : section 2
Problem number : 25
Date solved : Monday, January 27, 2025 at 05:49:37 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)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 68

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

\[ y(x)\to \sin \left (x^2\right ) \int _1^x\frac {1}{2} \cos \left (K[1]^2\right ) K[1]^3dK[1]-\frac {1}{8} \sin \left (2 x^2\right )+\frac {1}{4} x^2 \cos ^2\left (x^2\right )+c_1 \cos \left (x^2\right )+c_2 \sin \left (x^2\right ) \]