40.13.7 problem 27

Internal problem ID [6761]
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 : 27
Date solved : Monday, January 27, 2025 at 02:27:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(4*x^2*diff(y(x),x$2)+4*x^3*diff(y(x),x)+(x^2+1)^2*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, {\mathrm e}^{-\frac {x^{2}}{4}} \left (c_2 \ln \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 28

DSolve[4*x^2*D[y[x],{x,2}]+4*x^3*D[y[x],x]+(x^2+1)^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {x^2}{4}} \sqrt {x} (c_2 \log (x)+c_1) \]