Additional Mathematics 0606 / Straight-line graphs / 3.523.52: Differential equations from d2ydx2\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}dx2d2y0606/22/O/N/21 — Question 7 · 6 marksMark as done · Save for later · Show all solutions(a)Given d2ydx2=ex2+1(x2+1)2\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}=e^{x^{2}}+\dfrac{1}{(x^{2}+1)^{2}}dx2d2y=ex2+(x2+1)21 for ∣x∣<12|x|<\tfrac{1}{2}∣x∣<21, and dydx=2\dfrac{\mathrm{d}y}{\mathrm{d}x}=2dxdy=2 when x=0x=0x=0, find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}dxdy.[3]▸ Answer(b)Find yyy given y=4y=4y=4 when x=0x=0x=0.[3]▸ Answer▸ Official mark scheme← 3.51: Linear law: e2ye^{2y}e2y against x2x^{2}x23.53: Linear law: yyy against log(x+12)\log(x+\tfrac{1}{2})log(x+21) →
