83.49.25 problem Ex 25 page 140

Internal problem ID [19638]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 25 page 140
Date solved : Tuesday, January 28, 2025 at 02:05:55 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=exp(2*x),y(x), singsol=all)
 

\[ y = \left (-x +c_2 \right ) {\mathrm e}^{2 x}+c_1 \,{\mathrm e}^{x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (e^x (-x+c_2)+c_3 e^{2 x}+c_1\right ) \]