83.30.3 problem 3

Internal problem ID [19382]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:36:24 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 24

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

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