Given the first order ordinary differential equation (t – 4) y*dt – t° (y² – 3)dy = 0. Show that the differential equation is separable equation u( y)dy = v(t)dt . (а) (b) Hence, solve the equation.

Q: Solve the separable differential equation Subject to the initial condition: y(0) = 9. y = 11x -…

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Q: find the differential equation of y =C1cos(w+C2), w is A PARAMETER

A: To find the differential equation.

Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

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Q: write answer as fraction -(1/2)^3

A: We know , (a/b)n = an/bn

Q: Find the Homogeneous Differential Equation of: (x2-xy+y2)dx + xydy=0

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Q: Find the general solution of the linear differential equation: dy dx + (5x + 1)y=e-52.

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Q: Q5) find the derivative 1. x = sin and y = sin+ cos if taken together, satisfy the differential…

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Q: a) Solve the differential equation UTM dy dr sin z y", y(7) = 0. UTMU UTMUTM UTM

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Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: dy 5. dt = e&-t)secy(1+ t²). %3D

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Q: Write the first-order differential equation in standard form. (Use yp for dy/dt.) dy dt = 7y + ty +…

A: The standard form of a first-order differential equation is dydt+g(t)y=h(t)or, y'+g(t)y=h(t)…

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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Q: Find the general solution for the differential equation 2x dx + coty (1+x²)dy = 0. %3D

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Q: = t?y – y + t? – 1, y (0) = 1 dt dy Solve the differential equation

A: Given: dydt=t2y-y+t2-1   We know that; ∫1ax+bdx=1alnax+b+C And The Power rule: ∫xndx=xn+1n+1+C ;…

Q: y" + 4y' + 5y = 260e-t sin (3t)

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Q: Find the integrating factor of the non-exact differential equation : (3x²y+6xy+y³) dx+3(x²+y²) dy=0

A: Given a differential equation, 3x2y+6xy+y3dx+3x2+y2dy=0. To find the integrating factor of the given…

Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: dx = x- y + 1 dt dy = y - x + 2 dt

A: Given: dxdt=x-y+1                       1dydt=y-x+2                       2 The above system of…

Q: d²y (2) Check that y = sint satisfies the differential equation dt2

A: We have to solve

Q: Find the function satisfying the differential equation 3/ – 4y = 6e"

A: Given the differential equation as y'-4y = 6e6t It is 1st order Linear Differential Equation Compare…

Q: Determine the solution of the 1st Ordered Differential Equation: 3(x² + y²)dx + x(x² + 3y² + 6y)dy =…

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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.