83.26.9 problem 9

Internal problem ID [19333]
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 : 9
Date solved : Tuesday, January 28, 2025 at 01:34:25 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 19

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

\[ y(x)\to \frac {e^x+c_2 x+c_1}{x^2} \]