40.13.15 problem 36

Internal problem ID [6769]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 36
Date solved : Monday, January 27, 2025 at 02:29:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(6+9*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = x^{2} \left (c_1 \sin \left (3 x \right )+c_2 \cos \left (3 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+(6+9*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-3 i x} x^2 \left (6 c_1-i c_2 e^{6 i x}\right ) \]