Revision: Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order Applied Mathematics 2 BE Civil Engineering Semester 2 (FE First Year) University of Mumbai
- Evaluate D 4 Y D X 4 + 2 D 2 Y D X 2 + Y = 0
- Find the Length of the Curve X = Y 3 3 + 1 4 Y from Y = 1 → Y = 2
- Solve ( 4 X + 3 Y − 4 ) D X + ( 3 X − 7 Y − 3 ) D Y = 0
- Solve D Y D X = 1 + X Y with Initial Condition X 0 = 0 , Y 0 = 0.2 by Taylors Series Method. Find the Approximate Value of Y for X= 0.4(Step Size = 0.4).
- Solve D 2 Y D X 2 − 16 Y = X 2 E 3 X + E 2 X − Cos 3 X + 2 X
- Show that ∫ π 0 Log ( 1 + a Cos X ) Cos X D X = π Sin − 1 a 0 ≤ a ≤ 1 .
- Evaluate ∫ ∫ ∫ ( X + Y + Z ) D X D Y D Z Over the Tetrahedron Bounded by the Planes X = 0, Y = 0, Z = 0 and X + Y + Z = 1.
- Find the Mass of Lamina Bounded by the Curves 𝒚 = 𝒙𝟐 − 𝟑𝒙 and 𝒚 = 𝟐𝒙 If the Density of the Lamina at Any Point is Given by 24 25 X Y
- In a Circuit Containing Inductance L, Resistance R, and Voltage E, the Current I is Given by L D I D T + R I = E .Find the Current I at Time T at T = 0 and I = 0 and L, R and E Are Constants.
- Evaluate ( 2 X + 1 ) 2 D 2 Y D X 2 − 2 ( 2 X + 1 ) D Y D X − 12 Y = 6 X
- A Resistance of 100 Ohms and Inductance of 0.5 Henries Are Connected in Series with a Battery of 20 Volts. Find the Current at Any Instant If the Relation Between L,R,E is L D I D T + R I = E
- Solve ( D 3 + 1 ) 2 Y = 0
- Solve ( D 3 + D 2 + D + 1 ) Y = Sin 2 X
- Solve the Ode ( D − 1 ) 2 ( D 2 + 1 ) 2 Y = 0
- Evaluate ∫ 1 0 ∫ X 2 0 Y E X D Y D X
- Evaluate ∫ 1 0 X a − 1 Log X D X
- Solve ( 1 + X ) 2 D 2 Y D X 2 + ( 1 + X ) D Y D X + Y = 4 Cos ( Log ( 1 + X ) )
- Find the Length of Cycloid from One Cusp to the Next , Where X = a ( θ + Sin θ ) , Y = a ( 1 − Cos θ )
- Solve ( D 2 − 3 D + 2 ) Y = 2 E X Sin ( X 2 )
- Using D.U.I.S Prove that ∫ ∞ 0 E − ( X + a 2 X 2 ) D X = √ π 2 E − 2 a , a > 0
- Solve ( D 2 + 2 ) Y = E X Cos X + X 2 E 3 X
- Evaluate ∫ 1 0 ∫ 1 − X 0 1 ∫ 1 − X − Y 0 1 ( X + Y + Z + 1 ) 3 D X D Y D Z
- Find the Mass of the Lemniscate 𝒓𝟐=𝒂𝟐𝒄𝒐𝒔 𝟐𝜽 If the Density at Any Point is Proportional to the Square of the Distance from the Pole .
- Solve X 2 D 3 Y D X 3 + 3 X D 2 Y D X 2 + D Y D X + Y X = 4 Log X
- Solve ( D 2 − 7 D − 6 ) Y = ( 1 + X 2 ) E 2 X
- Apply Rungee Kutta Method of Fourth Order to Find an Approximate Value of Y When X=0.4 Given that D Y D X = Y − X Y + X , Y = 1 𝒚=𝟏 𝒘𝒉𝒆𝒏 𝒙=𝟎 Taking H=0.2.
- Solve by Variation of Parameters ( D 2 Y D X 2 + 1 ) Y = 1 1 + Sin X
- Compute the value of ∫ 1.4 0.2 ( sin x − I n x + e x ) Trapezoidal Rule (ii) Simpson’s (1/3)rd rule (iii) Simpson’s (3/8)th rule by dividing Into six subintervals.
- Evaluate ∫ a √ 2 0 ∫ √ a 2 − Y 2 Y Log ( X 2 + Y 2 ) Dxdy by Changing to Polar Coordinates .
- Evaluate ∫ ∫ ∫ X 2 Y Z D Z D Y D Z Over the Volume Bounded by Planes X=0, Y=0, Z=0 and X a + Y B + Z C = 1
- Evaluate ∫ ∞ 0 E X 3 √ X D X
- Using Beta Functions Evaluate ∫ π 6 0 Cos 6 3 θ . Sin θ D θ
- Solve ( 2 Y 2 − 4 X + 5 ) D X = ( Y − 2 Y 2 − 4 X Y ) D Y
- Evaluate ∫ ∞ 0 3 − 4 X 2 D X
- Show that ∫ 1 0 X a − 1 Log X D X = Log ( a + 1 )
- Given ∫ X 0 1 X 2 + a 2 D X = 1 a Tan − 1 ( X a ) Using Duis Find the Value of ∫ X 0 1 X 2 + a 2
- Solve by Method of Variation of Parameters D 2 Y D X 2 + 3 D Y D X + 2 Y = E E X
- Solve by Method of Variation of Parameters : ( D 2 − 6 D + 9 ) Y = E 3 X X 2
- Solve by Variation of Parameter Method D 2 Y D X 2 + 3 D Y D X + 2 Y = E E X .
- Linear Differential Equation with Constant Coefficient‐ Complementary Function
- Particular Integrals of Differential Equation
- Cauchy’S Homogeneous Linear Differential Equation
- Legendre’S Differential Equation
- Method of Variation of Parameters
