Solve the Cauchy euler equation dy 3x2 d²y + 6x -6y 3+ Inx3 dy dx3 dx2 dx

Q: Find the general solution of dy d²y 6- dx2 + 12- dx fip - 8y = 21e2 dx3

A: General solution

Q: Find the Particular solution of the ODE d²y dy - 62-7y = -9e-2x, at y(0) = -2 and ỹ(0) = –13 dx2 dx

A: To find The particular solution of the given ODE.

Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: Find the general real solution of d3y/dx3 -dy/dx = x2 + 4 +e4x

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Q: Find the general solution of dy -2x6 dx y-4

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Q: Find the complete solution of dy + dz = 3z'ydz

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Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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Q: Determine the general solution of  3(3x²+y²)dx - 2xydy=0

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Q: Solve using (a) analytical method, (b) Euler's Method, dy=x²y - 1.1y

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Q: 3. Find the complete solution of 2xdy – y(x + 1)dx + 6y³dx = 0

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Q: Solve the given Bernoulli DE: 3y' + 3y/x = 2x4y4

A: A detailed solution is given below

Q: 2. Find the general solution to d²y dz² dy + 3y = e* dr

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Q: Determine the General Solution of ye2x dx = ( 4+e2x %3D ) dy

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Q: Find the general Solution of DES: x yy'= x +3y

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Q: Find the general solution of 3(3x2 + y2 )dx – 2xydy = 0.

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Q: 8. Find the general solution of (x2 + y2 + 1) dx + (x2 – 2xy) dy = А. х2 - у? - ху — 1%3D Сх В. х2 +…

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Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: Find the general solution of: ydx — х*dy 3D0. || -

A: Use variable separable to solve the differential equation. Note: We are allowed to solve one…

Q: Solve the Cauchy euler equation 3x2+ 6x-6y = 3 + Inx d²y + 6x2-6y = 3 + lnx³ dx3

A: In the given question we have to solve the given Cauchy Euler equation. Method: the Cauchy Euler…

Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: Find the general solution of dy/dx = (x - 4) / (6 - 5x + x^2). O y = 2 In(x - 2) - In (x - 3) + C y…

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Q: 11. Find the general solution of (x – 2y)dx – (2x + 5y)dy = 0. | x2 a. 쭉-2y + 5y2 =C b. x2 – 4y + y2…

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Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

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Q: use the Lagrangian method to solve: U=x1^(1/2)x2^(1/2) subject to 50=5x1+10x2

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Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: 2. Find the general solution of d²y dy +5 dx² dx -6y= = : 0

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Q: Find the general solution of +3 d² y dx3 + 2x² % + 2x + d²y dx2 dy + 4y = 10x¬1 %3D

A: The solution is given as

Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: Find the general solution of 2y"+3y+y=3sin.x+xe"

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Q: Find the solution to the Bernoulli equation. 1 xay từ you Oy³ = 1+ CX-3 Oy³ = 1+ Cx³ Oy³ = Cx³-1…

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Q: Find the family of solutions of the equation (x2y5 + y3)dx + (x3y4 + x)dy = 0

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: dy + ydx %3D = 3x²y?dx,

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Q: 3. Find the general solutions of, dy _ x+ y dx х-у, a.

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Q: Find the general solution of d³y d²y dy + 4 + 10y = –24e* dx +9- dx3 dx²

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Q: Show that the homogenous equation (Ax + By) ⅆx + (Cx + Dy) ⅆy = 0 Is exact if and only if B = C.…

A: Please refer the attached image for complete solution.

Q: Solve the dff oq dy 3x寸票-5-2 %3D

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Q: dy dx + 3x²y = 6x²

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Q: Determine the solution of (2x - 3y + 2)dx + (2x - 3y + 1)dy = 0. a. 10x + 10y + ln(10x - 15y + 8)2…

A: Simply put z= 2x-3y and solve .

Q: 4. Find the general solution of (x3 + y³) dx = 3xy² dy = Cx = Cx А. -Зx3 + 2yз В. 7x3 + 2у3 С. -бх3…

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Q: Determine the General Solution of ye2x dx = ( 4+e2x ) dy %3D

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Q: 2. Find the general solution of d³y dy dy 6- dr3 + 12 dx2 dx 8y = 21e2 -

A: To find- Find the general solution of  d3ydx3 - 6d2ydx2 + 12dydx - 8y = 21e2x

Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: Find the general solution of the lines 3y (즉 + 2-2)dx + (2x- 3 +1 )dy = 0 - 2 )dx + ( 2x - +1 )dy =…

A: x2+3y4-2dx+2x-y2+1dy=0To Find: The general solution of the lines.

Q: Solve the general solution of the given DE * dy = (-5x + y)² – 4 dx 3 (1+ ce6x ) 3 (1 – ce6*) y = 5x…

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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.