y'(π/4) + y'(-π/4) = -√2
y'(π/4) - y'(-π/4) = π - √2
y(π/4) - y(-π/4) = -√2
y(π/4) + y(-π/4) = π²/2 + 2
I.F = e∫tanxdx = eln|secx| = secx
∴y.secx = ∫(2x + x²tanx)secxdx = ∫2xsecxdx + ∫x²(secx.tanx)dx
ysecx = x²secx + λ ⇒ y = x² + λcosx
y(0) = 0 + λ = 1 ⇒ λ = 1
y = x² + cosx
y(π/4) = π²/16 + 1/√2; y(-π/4) = π²/16 + 1/√2
y(x) = 2x - sinx
y'(π/4) = π/2 - 1/√2; y'(-π/4) = -π/2 - 1/√2
y'(π/4) - y'(-π/4) = π - √2