15.16.7 problem 7

Internal problem ID [3227]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:26:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

\[ y = x^{2} \left (\ln \left (x \right ) c_{1} +c_2 +x \right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 19

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

\[ y(x)\to x^2 (x+2 c_2 \log (x)+c_1) \]