83.26.1 problem 1

Internal problem ID [19325]
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 (C) at page 93
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:34:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+y&=3 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

\[ y \left (x \right ) = \sqrt {x}\, \sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_{2} +\sqrt {x}\, \cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_{1} +x^{2} \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 47

DSolve[x^2*D[y[x],{x,2}]+y[x]==3*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} \left (x^{3/2}+c_1 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )\right ) \]