83.15.1 problem 1

Internal problem ID [19186]
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 (G) at page 45
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:11:51 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+5*diff(y(x),x)-2=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (\left (2 c_{1} -c_{2} \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_{1} +2 c_{2} \right )\right ) {\mathrm e}^{2 x}}{5}+\frac {2 x}{5}+c_3 \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 47

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]+5*D[y[x],x]-2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} \left (2 x-(c_1-2 c_2) e^{2 x} \cos (x)+(2 c_1+c_2) e^{2 x} \sin (x)\right )+c_3 \]