83.41.12 problem 3

Internal problem ID [19492]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:46:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 20

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

\[ y(x)\to -\left (\left (x^2-1\right ) (c_2 \log (x)+c_1)\right ) \]