Solve the following ODEs by making an appropriate change of variable: 1-3y - 9x (a) (y² − x²) dy -2ry, (b) dr 1+ y + 3x dy dz =

Q: x-2X x+ X-6

A: Here we have to calculate the givne limit.  =limx→2x2-2xx2+x-6

Q: In (メ+リ1+x2 dx

A:

Q: y=1+Jx+5

A:

Q: x2−5x=0

A: GIVENx2-5x=0

Q: Determine whether the following is an equation or an expression.   2/x=4/3x+1/3

A:

Q: Solve for A. 1 0 0 1 2 -1 -1 1 A =

A:

Q: |4x – x² dx

A: Given query is to find the value of integral.

Q: 14 x= F X D 5 E 12 B A

A:

Q: Solve (2y +5)dx = 6dy O a. y = 3In(2x+5)+ c O b. x = 3In(2y +5)+c x =- In(2y+5) +c O d. x =…

A: Given that          (2y + 5)dx = 6dy Now we solve this differential equation.

Q: X+y=2 3x-2y=1

A: Given: X+y=2 3x-2y=1

Q: solve for (D³ -9D)y=0

A: If roots m1,m2,...,mn of the auxiliary equation is real and distinct then complete solution is…

Q: = 4 y = 2x – 1 :-y

A: Topic - linear equation In two Variables

Q: Solve for x: 2x – 3y = 6; y=4

A:

Q: xdx 4+²- x

A: We need to use integration by substitution technique. In integration by substitution technique, we…

Q: i= (2,-1) Suppose %3D and Find 3 - 2ui.

A: Given vector

Q: d. √³|x² – 3x − 4|dx - -

A:

Q: S2x√6x- 6x-x² dx =

A: To find out the integration of the given expression.

Q: Solve for y.   5/2y - 7/3y = 1

A:

Q: Solve for y X2 =9e?y

A: Given: x2=9e2y As we know that the exponent rule: lnm=x⇔m=ex So, we can also write as:…

Q: Determine all solutions. y = xy² - √x² + y²7

A:

Q: Evaluate:

A: To Determine: Find the integral

Q: Solve (2y + 5)dx = 6dy O a. x = 12In(2y+ 5)+ c O b. y = 3In(2x+5) + c C.x =-In(2y +5) + c O d. x =…

A: Given (2y+5)dx = 6dydx6 = dy2y+5

Q: 2メy dx +x°dy=o

A: Let's find.

Q: D dx = 4x + C

A:

Q: X 23 y + 4y = 0

A: Solving second order differential equation:-