40.13.14 problem 35

Internal problem ID [6768]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 35
Date solved : Monday, January 27, 2025 at 02:29:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y&=\left (3 x +2\right ) {\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

dsolve((x+1)*diff(y(x),x$2)-(3*x+4)*diff(y(x),x)+3*y(x)=(3*x+2)*exp(3*x),y(x), singsol=all)
 

\[ y = \left (x +c_1 \right ) {\mathrm e}^{3 x}+\frac {\left (3 x +4\right ) c_2}{3} \]

✓ Solution by Mathematica

Time used: 0.542 (sec). Leaf size: 48

DSolve[(x+1)*D[y[x],{x,2}]-(3*x+4)*D[y[x],x]+3*y[x]==(3*x+2)*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (x+\frac {2}{3}\right )+\frac {c_1 e^{3 x+3}}{\sqrt {2}}-\frac {1}{9} \sqrt {2} c_2 (3 x+4) \]