12th Business Maths Weekly Test - 3 ( Differential Equations )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Differential Equations )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Solve x \(\frac{dy}{dx}\) + 2y = x⁴

Solvethe following differential equations: (4D²+4D−3)y=e^2x

Solve the following homogeneous differential equations.
\(x\frac { dy }{ dx } =x+y\).

An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x²+ y²)dy = xydx where x represents the number of units (in thousands). What is the total revenue function?

Solve: log\(\left( \frac { dy }{ dx } \right) \) = ax + by

Solve: \(\frac { dy }{ dx } \) + e^x+ye^x= 0

Solve the following:
\(x\frac { dy }{ dx } +2y={ x }^{ 4 }\)

Solve the following differential equations
\(\frac{d^2 y}{dx^2}-2k\frac{dy}{dx}+k^2y=0\)

If \(\frac { dy }{ dx } \) + y tan x = sin x and if y = 0 when x = \(\frac{\pi}{3}\) express y in terms of x.

Form the differential equation having for its general solution y = ax²+ bx

Solve the following:
\(\frac { dy }{ dx } +\frac { 3{ x }^{ 3 } }{ 1+{ x }^{ 2 } } y=\frac { 1+{ x }^{ 2 } }{ 1+{ x }^{ 3 } } \)

Solve the following differential equations (3D²+ D − 14)y=13e^2x

Solve the following:
\(\frac { dy }{ dx } +ycosx=sinxcosx\).

Solve (D²-3D+2)y =e^4x given y=0 when x=0 and x=1.

Solve the following differential equations (D²+D−6)y=e^3x+ e^3x

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12th Business Maths Weekly Test - 3 ( Differential Equations )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Differential Equations )-Aug 2020

Part - A

Generic 2 - Answer All Question

Solve x \(\frac{dy}{dx}\) + 2y = x4

Solvethe following differential equations: (4D2+4D−3)y=e2x

Solve the following homogeneous differential equations. \(x\frac { dy }{ dx } =x+y\).

An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x2 + y2)dy = xydx where x represents the number of units (in thousands). What is the total revenue function?

Solve: log\(\left( \frac { dy }{ dx } \right) \) = ax + by

Solve: \(\frac { dy }{ dx } \) + ex+yex = 0

Solve the following: \(x\frac { dy }{ dx } +2y={ x }^{ 4 }\)

Solve the following differential equations \(\frac{d^2 y}{dx^2}-2k\frac{dy}{dx}+k^2y=0\)

If \(\frac { dy }{ dx } \) + y tan x = sin x and if y = 0 when x = \(\frac{\pi}{3}\) express y in terms of x.

Form the differential equation having for its general solution y = ax2 + bx

Solve the following: \(\frac { dy }{ dx } +\frac { 3{ x }^{ 3 } }{ 1+{ x }^{ 2 } } y=\frac { 1+{ x }^{ 2 } }{ 1+{ x }^{ 3 } } \)

Solve the following differential equations (3D2 + D − 14)y=13e2x

Solve the following: \(\frac { dy }{ dx } +ycosx=sinxcosx\).

Solve (D2-3D+2)y =e4x given y=0 when x=0 and x=1.

Solve the following differential equations (D2+D−6)y=e3x + e3x

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Solve x \(\frac{dy}{dx}\) + 2y = x⁴

Solvethe following differential equations: (4D²+4D−3)y=e^2x

Solve the following homogeneous differential equations.
\(x\frac { dy }{ dx } =x+y\).

An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x²+ y²)dy = xydx where x represents the number of units (in thousands). What is the total revenue function?

Solve: \(\frac { dy }{ dx } \) + e^x+ye^x= 0

Solve the following:
\(x\frac { dy }{ dx } +2y={ x }^{ 4 }\)

Solve the following differential equations
\(\frac{d^2 y}{dx^2}-2k\frac{dy}{dx}+k^2y=0\)

Form the differential equation having for its general solution y = ax²+ bx

Solve the following:
\(\frac { dy }{ dx } +\frac { 3{ x }^{ 3 } }{ 1+{ x }^{ 2 } } y=\frac { 1+{ x }^{ 2 } }{ 1+{ x }^{ 3 } } \)

Solve the following differential equations (3D²+ D − 14)y=13e^2x

Solve the following:
\(\frac { dy }{ dx } +ycosx=sinxcosx\).

Solve (D²-3D+2)y =e^4x given y=0 when x=0 and x=1.

Solve the following differential equations (D²+D−6)y=e^3x+ e^3x