MHT CET202519 Apr 2025Evening ShiftMathematicsDifferential EquationsActual
The solution of dy d x =(x+ y )^2 is
Options
- A⁻¹(x+y)=x+c, where c is the constant of integration
- Bx+ y = x+ c , where c is the constant of integration
- Cx+ y = ⁻¹ x+ c , where c is the constant of integration
- Dx+ y = ⁻¹(x+ y )+ c , where c is the constant of integration
Correct answer
A. ⁻¹(x+y)=x+c, where c is the constant of integration
Step-by-step solution
Solve the differential equation d y d x = (x + y)^2 by substituting z = x + y . Differentiating the substitution with respect to x gives d z d x = 1 + d y d x , so d y d x = d z d x - 1 . Substituting into the original equation yields d z d x - 1 = z^2 , which rearranges to d z d x = 1 + z^2 . Separate variables: d z 1 + z^2 = d x , then integrate both sides: d z 1 + z^2 = d x . The left side is ⁻¹(z) , and the right side is x + c , where c is the integration constant. Thus, ⁻¹(z) = x + c , and substituting back z