83.37.7 problem 7

Internal problem ID [19452]
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 VIII (B) at page 128
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:44:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 35

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

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