Solve your IGNOU Doubts

Question:

Using the method of variation of parameters, solve the equation

$$\frac{d^2y}{dx^2} + a^2y = \sec ax.$

See Answer →

Question:

Solve: $\frac{dx}{y^2 + yz + z^2} = \frac{dy}{z^2 + zx + x^2} = \frac{dz}{x^2 + xy + y^2}$ .

See Answer →

Question:

Solve: $(D^2 + 5DD' + 5D'^2)z = x \sin (3x - 2y)$ .

See Answer →

Question:

Solve: $(y^2 + yz)dx + (z^2 + zx)dy + (x^2 + xy)dz = 0$ .

See Answer →

Question:

Solve the differential equation: $\frac{dy}{dx} = (x + y)^2$ . A particle falls from rest in a medium in which the resistance is $\lambda v^2$ per unit mass, v being the velocity of the particle at time t. Prove that the distance fallen in time t is $\frac{1}{\lambda} \ln \cosh (t\sqrt{g\lambda})$ , where g is the acceleration due to gravity.

See Answer →

Question:

Solve the differential equation: $\frac{dy}{dx} = (x + y)^2$ .

See Answer →

Question:

Using the method of undetermined coefficients, solve the differential equation:

$$(D^3 + 2D^2 - D - 2)y = e^x + x^2.$

See Answer →

Question:

Using Charpit's method, find the complete integral of the p.d.e.:

$$2xz - px^2 - 2qxy + pq = 0.$

See Answer →

Question:

Solve: $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ .

See Answer →

Question:

Find the integral surface of the p.d.e.:

$$(x - y)p + (y - x - z)q = z$

through the circle $z = 1, x^2 + y^2 = 1$ .

See Answer →

Question:

Suppose that a thermometer having a reading of $75^\circ\text{F}$ inside a house is placed outside where the air temperature is $15^\circ\text{F}$ . Two minutes later it is found that the thermometer reading is $30^\circ\text{F}$ . Find the temperature reading T(t) of the thermometer at any time t.

See Answer →

Question:

Apply the method of variation of parameter to solve the differential equation:

$$y'' + 6y' + 9y = \frac{1}{x^3} e^{-3x}, \quad x > 0.$

See Answer →

Question:

The Pfaffian equation $(2xy^2 + 2xy + 2xz^2 + 1)dx + dy + 2z \, dz = 0$ is integrable.

See Answer →

Question:

The solution of the differential equation

$\frac{dy}{dx} = y$ with $y(0) = 0$

exists, but is not unique.

See Answer →

Question:

$\sin x \frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$ in $]0, \pi[$ is a linear homogeneous equation

See Answer →

Question:

The solution of the differential equation $\frac{dy}{d} = y$ with $y(0) = 0$ exists, but is not unique.

See Answer →

Question:

State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example: $(5 \times 2 = 10)$
a) y² is an integrating factor of the differential equation: