83.47.6 problem Ex 6 page 86

Internal problem ID [19583]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 6 page 86
Date solved : Tuesday, January 28, 2025 at 01:59:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=2 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 22

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

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