83.26.5 problem 5

Internal problem ID [19329]
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 : 5
Date solved : Tuesday, January 28, 2025 at 01:34:18 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

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

\[ y \left (x \right ) = c_{2} x^{4}+\frac {x^{4} \ln \left (x \right )}{5}+\frac {c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 31

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

\[ y(x)\to \frac {1}{5} x^4 \log (x)+\left (-\frac {1}{25}+c_2\right ) x^4+\frac {c_1}{x} \]