AP EAMCET202315 May 2023Morning ShiftMathematicsDifferential EquationsActual
The substitution x=v y converts which one of the following differential equation to an equation solvabie by variable separable method?
Options
- A(y^2-2 x^2 y ) d x= (x^2-2 x y^2 ) d y
- Bx^2 d y-y d x= x^2+y^2 d x
- Cd y d x = y^2 x+ x y
- D(1+2 e^ x y )+2 e^ x y (1- x y ) d y d x =0
Correct answer
D. (1+2 e^ x y )+2 e^ x y (1- x y ) d y d x =0
Step-by-step solution
x=v y converts those differential equation to variable separable form which we have Homogenous function f(x, y)= d y d x of order zero ie each term should have equal power. Option (a) & (b) are not homogeneous. Hence they are incorrect option. Option (c) have homogeneus function of order 1 because d y d x = y^2 x+ x y =f(x, y) . Hence option (c) is also not correct. Option (d) is correct because it have homogenous function of order zero d y d n =f(x, y)= - (1+2 e^ x y ) 2 e^ x y (1- x y )