dy 18. x = y (log y-log x+1) (AMIETE, Summer 2004) dx Ans. log2= Cx 19. xy logdx+| y -x² log dy = 0 given that y (1) = 0 y 3 + log y = 1- 4e? -log 2y2 y 4y2

Q: Solve the following ordinary differential equations: 4x dx d²x dt dt² dx dt - 3=0

A:

Q: Solve the following differential equation: ?′′′ +2?′′ +5?′ −26?=0

A:

Q: x +y = x³ /y X-

A:

Q: Solve the following differential equation by using integrating factors. xy=9y-8x²

A: xy' =9y-8x2A first order linear ODE has the form of y'x+pxy=qxRewrite in the form of a first order…

Q: 4- Solve the following differential equation.) + QA=0 12

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Q: d. y'\ + у %3D0

A:

Q: 2xydx – V x² + y²dy = 0

A: The solution is given as

Q: COSX cy?+) y2 dy e 8. COSX Cotx

A:

Q: 3. х — + 6у %3D 3хуз dx

A:

Q: (メ+ッ)dx + (x4ッ)dy =。 d x dy x yz x?y

A:

Q: a dß + B da + aß(3 da + dB) =0

A:

Q: Identify the type of differential equation (noting the best way to solve them): xy + y = =/=/2 y²

A: The given differential equation is xy'+y=1y2 We have to identify the type of given differential…

Q: = 2x- y dx

A:

Q: dy dx + 2y = x³e-2x

A: The given differential equation is: dydx+2y=x3e-2x

Q: a) Solve the following differential equation &y dªy 8- + 16y = 9e2 dx4 dr? by using the method of…

A:

Q: dy - 2y = x³ cosec 2x dx

A: To solve the below differential equation. xdydx−2y=x3csc2x

Q: D6 tan x+In yd - tan xdy =0

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.