83.25.3 problem 3

Internal problem ID [19323]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (B) at page 83
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:34:06 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 24

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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