83.31.4 problem 4

Internal problem ID [19396]
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 (E) at page 112
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:37:16 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 23

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

\[ y \left (x \right ) = \frac {\ln \left (2\right )}{4}+\frac {\ln \left (-{\mathrm e}^{-2 x} c_{1} +2 c_{2} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.384 (sec). Leaf size: 65

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

\begin{align*} y(x)\to \frac {1}{4} \left (-\log \left (e^{2 x}\right )+\log \left (-e^{2 x}+2 e^{c_1}\right )\right )+c_2 \\ y(x)\to \frac {1}{4} \left (\log \left (-e^{2 x}\right )-\log \left (e^{2 x}\right )+4 c_2\right ) \\ \end{align*}