83.19.1 problem 1

Internal problem ID [19158]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (B) at page 55
Problem number : 1
Date solved : Monday, March 31, 2025 at 06:50:13 PM
CAS classification : [_separable]

\begin{align*} y&=3 x +a \ln \left (y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.222 (sec). Leaf size: 43

ode:=y(x) = 3*x+a*ln(diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 3 x +a \ln \left (3\right ) \\ y &= 3 x +a \left (\ln \left (3\right )+\ln \left (-\frac {1}{-1+{\mathrm e}^{\frac {-3 c_1 +3 x}{a}}}\right )\right ) \\ \end{align*}

✓ Mathematica. Time used: 3.745 (sec). Leaf size: 29

ode=y[x]==3*x+a*Log[D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -a \log \left (\frac {1}{3} e^{-\frac {3 x}{a}}-\frac {c_1}{a}\right ) \]

✓ Sympy. Time used: 0.460 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*log(Derivative(y(x), x)) - 3*x + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = a \left (\log {\left (\frac {a e^{\frac {3 x}{a}}}{C_{1} e^{\frac {3 x}{a}} + a} \right )} + \log {\left (3 \right )}\right ) \]