83.12.3 problem 3

Internal problem ID [19175]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (D) at page 37
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:10:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=15 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)+2*diff(y(x),x)-15*y(x)=15*x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\left (\left (x^{2}+\frac {4}{15} x +\frac {38}{225}\right ) {\mathrm e}^{5 x}-{\mathrm e}^{8 x} c_{2} -c_{1} \right ) {\mathrm e}^{-5 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+2*D[y[x],x]-15*y[x]==15*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x^2-\frac {4 x}{15}+c_1 e^{-5 x}+c_2 e^{3 x}-\frac {38}{225} \]