BMTC-132 English Medium Solved Assignment 2026

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BMTC-132 English Medium Solved Assignment 2026 Available

1. State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example:

(5 * 2 = 10)

a) y ^ 2 is an integrating factor of the differential equation: 6xy * dx + (4y + 9x ^ 2) * dy = 0

b) The solution of the differential equation (dy)/d = y with y(0) = 0 exists, but is not unique.

c) in 10, pi [ is a linear homogeneous equation. sin x * (d ^ 2 * y)/(d * x ^ 2) + d/dx (y) + y = 0

d) The solution of the differential equation with y(0) = 0 exists, but is not unique. d/dx (y) = y

e) The Pfaffian equation (2x * y ^ 2 + 2xy + 2x * z ^ 2 + 1) * dx + dy + 2z * dz = 0 is integrable.

2. a) Apply the method of variation of parameter to solve the differential equation: x > 0 (5) y^ * + 6 * y’ + 9y = 1/(x ^ 3) * e ^ (- b * x) .

b) Suppose that a thermometer having a reading of 75 deg * F inside a house is placed outside where the air temperature is 15 deg * F . Two minutes later it is found that the thermometer reading is 30 deg * F Find the temperature reading T(t) of the thermometer at any time t.

3. a) Find the integral surface of the p.d.e: (x – y) * p + (y – x – z) * q = z through the circle z = L x ^ 2 + y ^ 2 = 1

b) Solve: (x ^ 2 * y – 2x * y ^ 2) * dx – (x ^ 3 – 3x ^ 2 * y) * dy = 0

4.a) Using Charpit’s method, find the complete integral of the p.d.e.: 2xz-px-2qxy+pq=0.

b) Using method of undetermined coefficients, solve the differential equation: (D ^ 2 + 2D ^ 2 – D – 2) * y =e^ * +x^ 2 .

c) Solve the differential equation: d/dx (y) = (x + y) ^ 2

5. a) 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 1/lambda * ln(cosh(t * sqrt(g*lambda))) where g is the acceleration due to gravity.

b) Solve: (y ^ 2 + yz) * dx + (z ^ 2 + zx) * dy + (y ^ 2 – xy) * dz = 0

6. a) Solve: (D^ 2 +SDD^ prime +SD^ prime2 ) z = x * sin(3x – 2y) .

b) Solve: (dx)/(y ^ 2 + yz + z ^ 2) = (dy)/(z ^ 2 + zx + x ^ 2) = (dz)/(x ^ 2 + xy + y ^ 2)

7. a) Using the method of variation of parameters, solve the equation

(d ^ 2 * y)/(d * x ^ 2) + a ^ 2 * y = sec(ax)

b) Solve (p + q)(px + qy) = 1 using Charpit’s method.

c) Solve: d/dx (y) = 1/(x + y + 1)

8. a) Solve: (D ^ x – D * D’ – 2D) * z = sin(3x + 4y) + e ^ (2x + y)

b) Use the method of variation of parameters to solve the following differential equation:

y^ prime prime – 2 * y’ + y = (12e ^ x)/(x ^ 3) .

9. a) Solve: x^ 2 y^ prime prime – 2x * y’ – 4y = x ^ 2 + 2 * ln(x) .

b) Solve the equation (7y – 3x + 3) * dy + (3y – 7x + 7) * dx = 0

10. a) Using the method of undetermined coefficients, solve the equation

(d ^ 2 * y)/(d * x ^ 2) – 3 * d/dx (y) + 2y = 4x ^ 2

b) Using Charpit’s method, solve the equation x * p ^ 3 – y ^ 2 * p + y ^ 2 * q = 0