Example 9: Obtain the differential equation of the co-axial circles of the svstem x² +y² + 2ax+c² = 0 where c is a constant and 'a' is a variable.

Q: Construct the differential equation of the family of curves xy=C(x-1)2 where C is an arbitrary…

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Q: dy +y 4)/2=x

A: Consider the following substitution: xy=u   ⇒   xdydx+y=dudx        and        y=ux

Q: Obtain the differential equation of the family of circles having their centers on the x-axis.…

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Q: 2) The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is…

A: a) The initial amount in the bank account is P=$1000. The rate of increment of the amount is…

Q: the indicial equation of the differential equation xy'' -x2y'+(1+2x)y=0

A: Question from differential equations.

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Find a homogeneous differential equation that is equivalent to the differen- tial equation 5t³y" +…

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Q: The equations listed below are not exact differentials. Find for each equation an integrating…

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Q: Solve for Linear Differential Equation of Order n: x^2y′′+(y′)^2−2xy′=0

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Q: Find complementary function of the differential equation  (D2 + 52)y = sin3x

A: The differential equation is D2+52y=sin3x.

Q: (x²+y)dx + dy 0

A: This linear differential equation

Q: A slope field shows that the slope at the point (1, 1) is 6. Does this slope field represent the…

A: Given yr = 4x +2y

Q: find the degree of the differential equation y''-12cosec y= 0   3 1 4 or 2

A: The order of the differential equation is 2.

Q: Sketch the direction or slope field of the differential equation. Be sure to show any “trends" and…

A: Given differential equation is y'=x-2y+1                   (i) Direction field of the given eq. (i)…

Q: The differential equation 4y"- siny y' + 3y = O is a linear equation. :Select one True False

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Q: Match the differential equation with its direction field. y'- sin(10x) sin(10y) 20) -0.3 1-0.2 1…

A: Remark: We know that the slope field is a graphical representation of a differential equation. This…

Q: 3ysinxdx/dy-2xycosx=0, Find exact differential equations

A: Given  3ysinxdx/dy-2xycosx=0

Q: Example 11 : Find the equation of the curve satisfying the differential eguatio- dy (1+x?)+2xy= 4x²…

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Q: The slope field for the equation y' = -x -y is shown below On a print out of this slope field,…

A: The slope field for the equation y'=-x-y passes through 1,0

Q: Sketch the slope field and some representative solution curves for the given differential equation.…

A: We are given the second order linear differential equation. y"=x+y. or  d2ydx2=x+y....(1) We need do…

Q: Find the differential equation of All parabolas whose axis is parallel to the y-axis. Draw at least…

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