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Subject: Applied Mathematics, asked on 24/11/22

R620 800 is invested for 4 years at 8% p.a compound interest. What will be the total of interestbe at the end of the 4 years? (NB use the compound interest tables provided or work to three decimal places only

Subject: Applied Mathematics, asked on 3/10/22

3 ( 1 + x2 ) y' = 2x??(??^3 ? 1)
Follow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.

Subject: Applied Mathematics, asked on 3/10/22

y' = y ( xy^3 - 1 )
Follow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.

Subject: Applied Mathematics, asked on 3/10/22

xy' - ( 1 + x ) y = xy^2
Follow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.

Subject: Applied Mathematics, asked on 3/10/22

2y dx + x [ x^2ln(y) - 1] dy = 0
Follow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.

Subject: Applied Mathematics, asked on 3/10/22

xy dx + (x^2 - 3y) dy =0
Follow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.

Subject: Applied Mathematics, asked on 3/10/22

y' = y - xy^3 e^-2x
Folllow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.

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