83.47.2 problem Ex 2 page 80

Internal problem ID [19579]
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 2 page 80
Date solved : Tuesday, January 28, 2025 at 01:59:52 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

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

\[ y \left (x \right ) = \frac {3 \ln \left (x \right ) x^{3}+9 c_{2} x^{3}-3 \ln \left (x \right )+9 c_{1} -1}{9 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,2}]-2*y[x]==x^2+1/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 \left (x^3-1\right ) \log (x)+(-1+9 c_2) x^3-1+9 c_1}{9 x} \]