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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-FP-DE1-0011 markL1 FoundationNon-calculatorIntegrating factor
The integrating factor for dydx+3y=ex\frac{dy}{dx}+3y=e^x is ekxe^{kx}. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-G012 marksL1 FoundationNon-calculatorIntegrating factor
The integrating factor for dydx+2yx=x\frac{dy}{dx}+\frac{2y}x=x is xkx^k. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-Q011 markL1 FoundationNon-calculatorIntegrating factor
The integrating factor for dydx+P(x)y=Q(x)\frac{dy}{dx}+P(x)y=Q(x) is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-X011 markL1 FoundationNon-calculatorIntegrating factor
Find the integrating factor for dydx+2y=ex\frac{dy}{dx}+2y=e^x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-X032 marksL1 FoundationNon-calculatorSolving
Solve dydx=2y\frac{dy}{dx}=2y with y(0)=3y(0)=3. Find y(1)y(1) exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-0042 marksL2 StandardNon-calculatorIntegrating factor
For xdydx+3y=x2x\frac{dy}{dx}+3y=x^2, which is the integrating factor?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-X023 marksL2 StandardNon-calculatorSolving
Solve dydx+yx=1\frac{dy}{dx}+\frac yx=1 (x>0x>0) with y=2y=2 when x=2x=2, and find yy when x=1x=1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-X041 markL2 StandardNon-calculatorIntegrating factor
Find the integrating factor for dydx−yx=x\frac{dy}{dx}-\frac yx=x, x>0x>0.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-X052 marksL2 StandardNon-calculatorSolving
dydx+2y=4\frac{dy}{dx}+2y=4 with y(0)=0y(0)=0. Find the limiting value of yy as x→∞x\to\infty.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-0024 marksL3 ExamNon-calculatorSolving
Solve dydx+yx=3x\frac{dy}{dx}+\frac yx=3x with y=2y=2 at x=1x=1. Give yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-0034 marksL3 ExamNon-calculatorSolving
dydx−2y=4\frac{dy}{dx}-2y=4, y(0)=1y(0)=1. Find the exact value of yy when x=ln⁡2x=\ln2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE1-0055 marksL4 ChallengingCalculatorSolving
cos⁡xdydx+ysin⁡x=cos⁡2x\cos x\frac{dy}{dx}+y\sin x=\cos^2x with y=2y=2 at x=0x=0. Find yy when x=πx=\pi (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme