ordinary differential equations

Consider two Ordinary Differential Equations (ODEs): P: $ \dfrac{dy}{dx} = \dfrac{x^4 + 3x^2 y^2 + 2y^4}{x^3 y} $ Q: $ \dfrac{dy}{dx} = -\dfrac{y^2}{x^2} $ Which one of the followi...

The solution of the differential equation $\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0$ is expressed as 𝑦 = 𝐶 1 𝑒 2.5𝑥 + 𝐶 2 𝑒 𝛼𝑥 + 𝐶 3 𝑒 𝛽𝑥 , wher...

Consider the differential equation $${{dy} \over {dx}} = 4(x + 2) - y$$ For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a ste...

Water is following at a steady rate through a homogeneous and saturated horizontal soil strip of $$10$$m length. The strip is being subjected to a constant water head $$(H)$$ of $$...

The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \right)}^3} + {y^2}} = 0$$ are respectively

A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^ \circ }$$c. What will be the temperature of the body at the...

Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \right)y = q\left( t \right){y^n},\,\,n > 0$$ will be

For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is

The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,

The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {x,y} \right)dy = 0\,\,$$ to be exact is