y? 9. dy y² + 4y + 8

Q: y (4) + y" +y" = 0, where y(0) = y'(0) = y″(0) = 0, y″(0) = 1

A:

Q: 3 Find y" for y = 5 + y" =D

A:

Q: 丰 ZZ= ? А. X В. U С.Т OA O B

A:

Q: dy 2ry = 1+ y? , y(2) = 3 da

A:

Q: If y=x*, then y' (1) = A) 6 B) 12 C) e6+12 D) In(6) + 1

A: Given; if y = x6x , then y'(1)=?

Q: rvdxdy ( R nd x 2 0, y 2

A:

Q: y" – y' – 12y = -24e' where y(0) = 5, y'(0) = 3 |

A: Given differential equation y''−y'−12y=−24et where y0=5, y'0=3 We have to find the given…

Q: - y" – 2y" + y' = 2 – 24e* + 40e, y'(0) = }, y"(0) = - y(0) = ;, 9. 2

A:

Q: r4 & 2Vz& /4z=x? 2. JJJO & 0 & 0 Jo & 0 & 0 S dydxdz

A:

Q: 2 y+ 3 dy y + 5y + 6

A:

Q: S (a? - y)"y dy

A:

Q: d?y Determine if: 2x2 – xy + 5y2 = 7 dx2

A:

Q: dy If x? + y? = 16x, then dx 8+ x y 8. y 8+ x y 8- x D y

A:

Q: (V) - 22+ラソー dy 4ス+by+2 (vi) Sotwe 4e da +(ae +24) dy

A:

Q: 2. (D2 – 4)y = 0 when y(0) = 0, y' = 3

A:

Q: If y = 3(8 – y) and y(1) = 10 what is y(0)? %D y(0) = %3D

A:

Q: y ce + 3r O y'+6y 2t (t+ 1) O y'+2y = / (1+ 6) 3. y'-2y 61 (t- 1) O y'+ 2y = 61 (1 + 1)

A:

Q: ($4y - 7y–12 dy. y' +y? - 6y Q.4 Evaluate

A: We have to use partial fraction to separate denominator and then take integration to obtain…

Q: 4) y – 4y = 8u(t – 3), y(0) = 2;

A:

Q: d²y 7. – 4y=-6e', y(0)=3; y'(0)=4 di? 2/2

A:

Q: r+ 2y = 4 3r + 8y %3D I =?

A: Simultaneous equations are two or more equations which involves two or more quantities that are…

Q: y" + 16y' = 128(t — 57/8); y(0) = 3, y' (0) = ( C

A:

Q: dy (y-4) (y +4y+16) 4. 32.

A: 4). To solve: ∫5y2-32y-4y2+4y+16dy Solution: Using partial fraction decomposition given integrand…

Q: w Dy ),-0 7 By b. Əw əz C. aw əz

A:

Q: dy 3. 9+y? メーNE _ xp

A:

Q: dy 4. х dr =x³ – 2y, given x =1 when 47 y=3 y3= - - 3 15x2

A:

Q: dy (c) - - 6. z2; y (1) = 10 dr 2 y [8 marks] %3D The answer is y

A:

Q: If y= x6* , then y' (1) = %3D A) 6 B) 12 C) e6+12 D) In(6) + 1

A:

Q: y² + 5 dy y²(y² + 25)

A:

Q: Q7// Evaluate y y2-64 dy

A:

Q: (y n?(1 + 3*) dy 1+ y? 2.

A:

Q: dy + 3x?y = 6x? dx y = 2 + Ce*3 y = 3 + Ce-x³ Option 1 Option 2 y = 3+ Ce* y = 2 + Ce-x³

A: It is given that, dydx+3x2y=6x2   It is known that whenever we have differential equation in 2…

Q: y/" – 4y' + 4y = 8 – 2e²", y(0) = 0, y'(0) = 1. -

A:

Q: x2y"+xy'+x?y=0, у-0,

A:

Q: -2 c3 4. Sí S S(6x? + 4y² – 12z²)dxdydz

A:

Q: [y(8y² -5)dy 4y* -5y? +5 1.

A: We can find the answer as below

Q: (a² + y²)dæ = 2y[(a² + y?)² + 4x]dy ?

A: First we find the integrating factor then solve this ODE

Q: 4y2 – 7y – 12 dy 17. \ y + 2)(y – 3)

A:

Q: -2 2 /y + 2 dy + √ ² [√y+2_y] dy

A:

Q: y" + 27y' + 7y = 0 + Ty = 0 %3D

A:

Q: 4. y" — 2y' + y = 4e¯t + 2et, where y(0) = −1, y'(0) = 2 2+

A:

Q: y? -dy (y2–4) 7

A: We have to find solution

Q: 1 Ifx+y= 6/x? – xy + y? = 7, then x3 + y³ = a) 13 b) 24 c) 42 d) 1

A: Simplification

Q: y" – 3y' + 2y = 4e2x, where y(0) = -3, y'(0) = 5

A:

Q: S SEV1+ y3 dydx =?

A:

Q: (3ry- 1) dr + (x³ + 6y – y?) dy = 0 y(0) = 3

A:

Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

A:

Q: y' – 2y = y², when y = 3 and x |0 =

A: