83.19.1 problem 1

Internal problem ID [19150]
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 : Thursday, March 13, 2025 at 01:45:47 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 55

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

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

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