differential equation

Consider differential equation $\frac{dy}{dx} + xy = x$ with the condition as y = 0 at x = 0. The value of y at x = 1.0 is ________ (rounded off to two decimal places).

Pick the CORRECT solution for the following differential equation $\frac{dy}{dx} = e^{x-y}$

Let y be the solution of the initial value problem y'' + 0.8y' + 0.16y = 0, where y(0) = 3 and y'(0) = 4.5. Then, y(1) is equal to ________ (rounded off to 1 decimal place).

Consider the differential equation given below. Using the Euler method with the step size (h) of 0.5, the value of y at x = 1.0 is equal to ________ (rounded off to 1 decimal place...

Pick the CORRECT solution for the following differential equation $\frac{d y}{d x}=e^{x-y}$

The second-order differential equation in an unknown function u: u(x, y) is defined as $\frac{\partial^2 u}{\partial x^2} = 2$. Assuming g:g(x), f: f(y), and h: h(y), the general s...

A 2m x 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentrat...

The differential equation, $\frac{du}{dt} + 2tu^2 = 1$, is solved by employing a backward difference scheme within the finite difference framework. The value of $u$ at the $(n-1)^{...

In the differential equation $\frac{dy}{dx}+\alpha\ x\ y =0, \alpha$ is a positive constant. If y = 1.0 at x = 0.0, and y = 0.8 at x = 1.0, the value of α is ________ (rounded off...

For the equation $\frac{d^3y}{dx^3} + x (\frac{dy}{dx})^{3/2} + x^2y = 0$ the correct description is

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

If k is a constant, the general solution of dy/dx - y/x = 1 will be in the form of

An ordinary differential equation is given below. $\left(\frac{dy}{dx}\right) (x \ln x) = y$ The solution for the above equation is (Note: K denotes a constant in the options)

Consider the ordinary differential equation $x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0$. Given the values of y(1) = 0 and y(2) = 2, the value of y(3) (round off to 1 decima...

Consider the following second-order differential equation: $y'' - 4y' + 3y = 2t - 3t^2$ The particular solution of the differential equation is

The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ is

The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is

Solution of the differential equation $$3y{{dy} \over {dx}} + 2x = 0$$ represents a family of

The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is

The degree of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{x^3} = 0\,\,$$ is

The solution of the differential equation $$\,{x^2}{{dy} \over {dx}} + 2xy - x + 1 = 0\,\,\,$$ given that at $$x=1,$$ $$y=0$$ is

Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$ given that $$y=0$$ and $$dy/dt=9$$ at $$t=0$$

The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$

The differential equation $${{{d^4}y} \over {d{x^4}}} + P{{{d^2}y} \over {d{x^2}}} + ky = 0\,\,$$ is

Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third place of decimal by the $${2^{nd}...