83.26.14 problem 14

Internal problem ID [19338]
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 : 14
Date solved : Tuesday, January 28, 2025 at 01:34:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y&=\left (1+x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-20*y(x)=(x+1)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} x^{4}+\frac {c_{1}}{x^{5}}-\frac {x^{2}}{14}-\frac {x}{9}-\frac {1}{20} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 33

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-20*y[x]==(1+x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^5}+c_2 x^4-\frac {x^2}{14}-\frac {x}{9}-\frac {1}{20} \]